I totally agree about the continuum - for the most part it is so strange from ordinary experience that it seems like a binary shift, but yes, I think it is important to see it as a continuum (perhaps a bit stepped/quantized, but not sure).
Fascinating that you managed to get there with the tapping game doing speed drills. I often had ideas but it was before common MRIs and other technology that we had for examining brain functions at high resolution. That is something you could get into an MRI, and/or an intense electrode-sensor grid and measure! So, yes, I'd think some funding might be possible. I know academic funding is it's own labrynthine nightmare, so probably best to be in a program supported by an experienced professor/primary researcher who knows the ropes. OTOH, if you can get to show some results that improve performance, perhaps approaching some top pro sports team owners for funding? (I know if I were a billionaire with a team, I'd be interested in something that could give us an edge!) The question is whether you can generate useful results soon, and in what sport. You seem to have made a lot of progress in eSports, there might be some money there... Let me know if you're interested in chatting offline (is there a DM function here to exchange contact info w/o publishing?)